On reductibility of degenerate optimization problems to regular operator equations

We present an application of the $p$-regularity theory to the analysis of non-regular (irregular, degenerate) nonlinear optimization problems. The $p$-regularity theory, also known as the $p$-factor analysis of nonlinear mappings, was developed during last thirty years. The $p$-factor analysis is based on the construction of the $p$-factor operator which allows us to analyze optimization problems in the degenerate case. We investigate reducibility of a non-regular optimization problem to a regular system of equations which do not depend on the objective function. As an illustration we consider applications of our results to non-regular complementarity problems of mathematical programming and to linear programming problems.